URGENT - differntial equation

[sheffield]

Hello, I have the following equation:


\(\displaystyle \frac{1}{2}{\sigma ^2}{S^2}{G_{11}} + rS{G_1} - rG = 0 \) (1)


I know that it will give give me a general solution of:


\(\displaystyle G = {a_1}S + {a_2}{S^{\frac{{2r}}{{{\sigma ^2}}}}} \) (2)


And then I use some conditions to find out the values of a1 and a2.


However I don't know how to go from the initial equation to its general solution. (from (1) to (2) )
Don't know differential equations at all, I study social sciences (and I try to understand dif equations myself) so an explicit way to derive the general solution will be very helpfull.


It's a matter of 48 hrs urgency. Thanks.

 

[stapel]

I have the following equation:

\(\displaystyle \frac{1}{2}{\sigma ^2}{S^2}{G_{11}} + rS{G_1} - rG = 0 \) (1)

I know that it will give give me a general solution of:

\(\displaystyle G = {a_1}S + {a_2}{S^{\frac{{2r}}{{{\sigma ^2}}}}} \) (2)

...I don't know how to go from the initial equation to its general solution....

It's a matter of 48 hrs urgency. Thanks.

Um... What do you mean by "a matter of 48 hrs urgency"? Are you asking us to complete your take-home test or something?

 

[Deleted member 4993]

Hello, I have the following equation:


\(\displaystyle \frac{1}{2}{\sigma ^2}{S^2}{G_{11}} + rS{G_1} - rG = 0 \) (1)


I know that it will give give me a general solution of:


\(\displaystyle G = {a_1}S + {a_2}{S^{\frac{{2r}}{{{\sigma ^2}}}}} \) (2)


And then I use some conditions to find out the values of a1 and a2.


However I don't know how to go from the initial equation to its general solution. (from (1) to (2) )
Don't know differential equations at all, I study social sciences (and I try to understand dif equations myself) so an explicit way to derive the general solution will be very helpfull.


It's a matter of 48 hrs urgency. Thanks.

I cannot make head-or-tail out of the equation given, it's probable relation with the topic subject and the answer given!!!!